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NASA NTRS2017

A Fast Hybrid (3-D/1-D) Model for Thermal Radiative Transfer in Cirrus via Successive Orders of Scattering

We investigate the impact of cirrus cloud heterogeneity on the direct emission by cloud or surface and on the scattering by ice particles in the thermal infrared (TIR). Realistic 3-D cirri are modeled with the 3DCLOUD code, and top-of-atmosphere radiances are simulated by the 3-D Monte Carlo radiative transfer (RT) algorithm 3DMCPOL for two (8.65 micrometers and 12.05 micrometers) channels of the Imaging Infrared Radiometer on CALIPSO. At nadir, comparisons of 1-D and 3-D RT show that 3-D radiances are larger than their 1-D counterparts for direct emission but smaller for scattered radiation. For our cirrus cases, 99% of the 3-D total radiance is computed by the third scattering order, which corresponds to 90% of the total computational effort, but larger optical thicknesses need more scattering orders. To radically accelerate the 3-D RT computations (using only few percent of 3-D RT time with a Monte Carlo code), even in the presence of large optical depths, we develop a hybrid model based on exact 3-D direct emission, the first scattering order from 1-D in each homogenized column, and an empirical adjustment linearly dependent on the optical thickness to account for higher scattering orders. Good agreement is found between the hybrid model and the exact 3-D radiances for two very different cirrus models without changing the empirical parameters. We anticipate that a future deterministic implementation of the hybrid model will be fast enough to process multiangle thermal imagery in a practical tomographic reconstruction of 3-D cirrus fields.

radiative transfer↗

DOE OSTI2021

Accelerated impurity solver for DMFT and its diagrammatic extensions

Here, we present ComCTQMC, a GPU accelerated quantum impurity solver. It uses the continuous-time quantum Monte Carlo (CTQMC) algorithm wherein the partition function is expanded in terms of the hybridisation function (CT-HYB). ComCTQMC supports both partition and worm-space measurements, and it uses improved estimators and the reduced density matrix to improve observable measurements whenever possible. ComCTQMC efficiently measures all one and two-particle Green's functions, all static observables which commute with the local Hamiltonian, and the occupation of each impurity orbital. ComCTQMC can solve complex-valued impurities with crystal fields that are hybridized to both fermionic and bosonic baths. Most importantly, ComCTQMC utilizes graphical processing units (GPUs), if available, to dramatically accelerate the CTQMC algorithm when the Hilbert space is sufficiently large. We demonstrate acceleration by a factor of over 600 (100) in a simulation of δ-Pu at 600 K with (without) crystal fields. In easier problems, the GPU offers less impressive acceleration or even decelerates the CTQMC. Here we describe the theory, algorithms, and structure used by ComCTQMC in order to achieve this set of features and level of acceleration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Bidding Curve Design for Hybrid Power Plants with Uncertain Solar Forecast: Preprint

This paper presents a novel bidding curve design algorithm tailored for hybrid power plants (HPPs) to participate in the wholesale electricity market. Utilizing forecasts for photovoltaic (PV) generation and available battery power, our algorithm strategically computes the bidding curve to maximize HPP profit while adeptly managing the inherent uncertainty associated with PV power generation. In addition, the introduction of the penalty cost in HPP bidding curves provides the system operator a tool to effectively manage the system-level uncertainty that caused by HPPs. Numerical analysis through Monte Carlo simulations confirms that our bidding curve methodology outperforms the benchmark across various scenarios.

bidding curve↗

DOE OSTI2025

Bidding Curve Design for Hybrid Power Plants with Uncertain Solar Forecast

bidding curve↗

DOE OSTI2020

TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo

TurboRVB is a computational package for ab initio Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC) and diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions (WFs), capable of describing several materials with very high accuracy, even when standard mean-field approaches [e.g., density functional theory (DFT)] fail. The electronic WF is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal power with spin-singlet pairing or as a Pfaffian, including both singlet and triplet correlations. This WF can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) Ansatz, first proposed by Pauling and Anderson in quantum chemistry [L. Pauling, The Nature of the Chemical Bond (Cornell University Press, 1960)] and condensed matter physics [P.W. Anderson, Mat. Res. Bull 8, 153 (1973)], respectively. The RVB Ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. Therefore, its application to large systems is computationally feasible. The WF is expanded in a localized basis set. Several basis set functions are implemented, such as Gaussian, Slater, and mixed types, with no restriction on the choice of their contraction. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization (Jastrow and antisymmetric parts together) is made possible, thanks to state-of-the-art stochastic algorithms for energy minimization. In the optimization procedure, the first guess can be obtained at the mean-field level by a built-in DFT driver. The code was efficiently parallelized by using a hybrid MPI-OpenMP protocol, which is also an ideal environment for exploiting the computational power of modern Graphics Processing Unit accelerators.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Charge singlets and orbital-selective charge density wave transitions

The possibility of “orbitally selective Mott transitions” within a multiband Hubbard model, in which one orbital with large on-site electron-electron repulsion U 1 is insulating and another orbital, to which it is hybridized, with small U –1 , is metallic, is a problem of long-standing debate and investigation. In this paper we study an analogous phenomenon, the coexistence of metallic and insulating bands in a system of orbitals with different electron-phonon coupling. To this end, we examine two variants of the bilayer Holstein model: a uniform bilayer and a “Holstein-metal interface” where the electron-phonon coupling, λ, is zero in the “metallic” layer. In the uniform bilayer Holstein model, charge density wave (CDW) order dominates at small interlayer hybridization t 3 , but decreases and eventually vanishes as t 3 grows, providing a charge analog of singlet (spin liquid) physics. In the interface case, we show that CDW order penetrates into the metal layer and forms long-range CDW order at an intermediate ratio of inter- to intralayer hopping strengths, 1.4 ≲ t 3 /t ≲ 3.4. Furthermore, this is consistent with the occurrence of an “orbitally selective CDW” regime at weak t3 in which the layer with λ 1 ≠ 0 exhibits long-range charge order, but the “metallic layer” with λ –1 = 0, to which it is hybridized, does not.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Hybrid Particle Swarm-Interpolation Algorithm for Improved Critical Experiment Design

The typical goal of designing a critical experiment is twofold: a system that is both critical and optimized for some other value. This value could be an energy-integrated sensitivity, percent fissions in a certain energy range, or some other value that can be calculated by a transport code. By simulating different combinations of reflector, moderator, and fuel thicknesses a designer can identify such a desirable configuration. The domain of all possible combinations of these thicknesses is referred to as the experiment search space. As more dimensions are added, the search space increases in size exponentially. For a three-dimensional case, which includes three thickness values between zero and ten centimeters to the nearest tenth of a millimeter, a total of 1,000 3 , configurations exists. Rather than check each configuration individually, which would be extremely computationally expensive, it has been shown to be more efficient to use a conventional particle swarm optimization (PSO) algorithm to identify critical and optimal configurations. This work presents the theory and implementation of a novel hybrid PSO interpolation algorithm to perform these optimizations faster than a conventional PSO algorithm. To demonstrate this, an example optimization will be carried out by the conventional and hybrid PSO algorithms and their performances will be compared.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Impact of solvent forces and broken symmetry on the assembly of designed proteins at a liquid-solid interface

The era of protein design has enabled the creation of hybrid protein-inorganic interfaces, leading to both surface-directed self-assembly of de novo protein architectures and protein-directed formation of inorganic materials. However, the resulting patterns of protein assembly are often unexpected, implying that essential interactions are not accounted for in current design platforms. Here, we use high-speed atomic force microscopy (AFM) analyzed through machine learning to follow the assembly of protein nanorods in aqueous electrolytes on two types of mica exhibiting disparate symmetry elements, which are imprinted on the overlying hydration structure. Using Monte Carlo simulations, we reproduce the observed phases and show that an observed smectic phase, previously thought to be unstable for non-interacting rods in two dimensions, emerges when crystal symmetry introduces a directional bias. The findings demonstrate the importance of incorporating solvent forces as modulated by the hydration structure inherent to interfacial systems when designing protein assemblies at liquid-crystal interfaces. Coupling physics-based simulations that can account for these factors to de novo protein design algorithms can lead to improved design platforms for bio-inspired, hybrid materials.

bioinspired materials↗

NASA NTRS1988

Digital and optical shape representation and pattern recognition; Proceedings of the Meeting, Orlando, FL, Apr. 4-6, 1988

The present conference discusses topics in pattern-recognition correlator architectures, digital stereo systems, geometric image transformations and their applications, topics in pattern recognition, filter algorithms, object detection and classification, shape representation techniques, and model-based object recognition methods. Attention is given to edge-enhancement preprocessing using liquid crystal TVs, massively-parallel optical data base management, three-dimensional sensing with polar exponential sensor arrays, the optical processing of imaging spectrometer data, hybrid associative memories and metric data models, the representation of shape primitives in neural networks, and the Monte Carlo estimation of moment invariants for pattern recognition.

Juday, Richard D.↗

NASA NTRS2012

Progress Toward Affordable High Fidelity Combustion Simulations Using Filtered Density Functions for Hypersonic Flows in Complex Geometries

Significant progress has been made in the development of subgrid scale (SGS) closures based on a filtered density function (FDF) for large eddy simulations (LES) of turbulent reacting flows. The FDF is the counterpart of the probability density function (PDF) method, which has proven effective in Reynolds averaged simulations (RAS). However, while systematic progress is being made advancing the FDF models for relatively simple flows and lab-scale flames, the application of these methods in complex geometries and high speed, wall-bounded flows with shocks remains a challenge. The key difficulties are the significant computational cost associated with solving the FDF transport equation and numerically stiff finite rate chemistry. For LES/FDF methods to make a more significant impact in practical applications a pragmatic approach must be taken that significantly reduces the computational cost while maintaining high modeling fidelity. An example of one such ongoing effort is at the NASA Langley Research Center, where the first generation FDF models, namely the scalar filtered mass density function (SFMDF) are being implemented into VULCAN, a production-quality RAS and LES solver widely used for design of high speed propulsion flowpaths. This effort leverages internal and external collaborations to reduce the overall computational cost of high fidelity simulations in VULCAN by: implementing high order methods that allow reduction in the total number of computational cells without loss in accuracy; implementing first generation of high fidelity scalar PDF/FDF models applicable to high-speed compressible flows; coupling RAS/PDF and LES/FDF into a hybrid framework to efficiently and accurately model the effects of combustion in the vicinity of the walls; developing efficient Lagrangian particle tracking algorithms to support robust solutions of the FDF equations for high speed flows; and utilizing finite rate chemistry parametrization, such as flamelet models, to reduce the number of transported reactive species and remove numerical stiffness. This paper briefly introduces the SFMDF model (highlighting key benefits and challenges), and discusses particle tracking for flows with shocks, the hybrid coupled RAS/PDF and LES/FDF model, flamelet generated manifolds (FGM) model, and the Irregularly Portioned Lagrangian Monte Carlo Finite Difference (IPLMCFD) methodology for scalable simulation of high-speed reacting compressible flows.

Drozda, Tomasz G.↗

DOE OSTI2023

Studying the hadron structure with PANDA and CLAS using machine learning techniques

The hadron spectroscopy and structure are currently very active fields of research to study the non-perturbative regime of quantum chronodynamics. The first one studies the complex structure of excited hadrons by looking at their decay products, while the latter uses lepton scattering on nucleons. Both methods require reconstruction algorithms with great efficiency and good particle identification and background rejection rates. This work aims to provide these by either improving the existing methods or developing new ones. The first part of this document presents a feasibility study of a predicted hybrid charmonium state for the PANDA experiment. Lattice QCD calculations predict the ground state hybrid charmonium to be a spin exotic with quantum numbers of JP C = 1?+ at a mass of around 4.3 GeV with a width to be around 20 MeV. A machine learning based data analysis scheme is proposed to further improve the signal efficiency and the background reduction, alongside with improvements of the analysis software (PandaRoot), that are vital for this study. These improvements include a reworked clustering algorithm for the electromagnetic calorimeter (EMC) and an optimized monte carlo matching for neutral particles. The second part of this document is about studying the proton structure. A multidimensional study of the structure function ratio Fsin(?)LU /FUU has been performed for K±, based on the measurement of beam-spin asymmetries. It uses the high statistics data recorded with the CLAS12 spectrometer at Jefferson Laboratory. Fsin(?)LU is a twist-3 quantity that provides information about the quark gluon correlations in the proton. This document will present for the first time a simultaneous analysis of two kaon channels over a large kinematic range of z, xB , PT and Q2 with virtualities Q2 ranging from 1 GeV2 up to 8 GeV2 using machine learning techniques for improved particle identification.

Kripko, Aron↗

DOE OSTI2025

Direct NeTS sampling of nuclear graphite $S(α, β, T)$ in Serpent

For advanced reactor applications, Neural Thermal Scattering (NeTS) modules were developed to predict the thermal scattering law (TSL or $S(α, β, T)$) of a nuclear graphite neutron moderator. NeTS are multi-layer, feedforward artificial neural networks, which act as universal function approximators designed for TSL datasets. In this case, a 4-layer neural network with 164 neurons per layer is trained using FLASSH evaluated data in PyTorch and serialized as a torchscript dictionary to predict $S(α, β, T)$ on-the-fly. Relative, absolute and maximum percent deviations of NeTS from File 7 data generated using the FLASSH code are on the order of 0.01%, 0.1% and 1%, respectively, with low inference latencies of 0.000172 s per $S(α, β, T)$ at a given temperature. Capturing the full dimensionality of possible inelastic neutron-lattice interactions, NeTS functionality is embedded in the Serpent Monte Carlo code, where $S(α, β, T)_{NeTS}$ sampling is conducted on-the-fly and compared to ACE look-up-tables for predicting TREAT criticality. k-eff differences between sampling algorithms of 6 pcm are observed and are within the order of Monte Carlo uncertainty. Compared to discrete and continuous-energy ACE files (30 MB and 131 MB per temperature), the NeTS format is on the order of 200–300 kB for a continuous-temperature, interpolation-free representation of $S(α, β, T)$ and cross sections. NeTS-in-Serpent runtimes comparable with ACE look-up tables are achieved by scaling NeTS for high performance computing architectures with hybrid OpenMP + MPI parallelization. This work validates a novel, self-contained reactor physics framework for predictive cross sections, and demonstrates a general methodology for embedding modern machine learning libraries within existing neutronic analysis frameworks.

Nuclear Criticality Safety Program (NCSP)↗

NASA NTRS1992

Aerocapture and aeromaneuvering at Mars

This paper presents the results of a guidance analysis study for aerocapture and aeromaneuvering at Mars. A 4-state, near-optimal, hybrid guidance algorithm is derived for applications throughout the paper. It is based on the critical assumption that Loh's function remains constant between successive guidance updates. Besides the guidance algorithm, the paper presents a performance evaluation of guidance derived from estimated or 'navigated' spacecraft state, provided by an onboard navigation subsystem for real-time applications on Mars. For the performance evaluation, the spacecraft state is augmented by such parameters as the reference atmospheric density and scale-height, the banking angle and angle of attack for spacecraft control and the accelerometer measurement model errors. Finally, the paper examines also, the influence of random uncertainties in atmospheric density on aeroassisted maneuvers, by a Monte Carlo type of simulation.

Vijayaraghavan, A.↗

NASA NTRS2000

Filtering in Hybrid Dynamic Bayesian Networks

We implement a 2-time slice dynamic Bayesian network (2T-DBN) framework and make a 1-D state estimation simulation, an extension of the experiment in (v.d. Merwe et al., 2000) and compare different filtering techniques. Furthermore, we demonstrate experimentally that inference in a complex hybrid DBN is possible by simulating fault detection in a watertank system, an extension of the experiment in (Koller & Lerner, 2000) using a hybrid 2T-DBN. In both experiments, we perform approximate inference using standard filtering techniques, Monte Carlo methods and combinations of these. In the watertank simulation, we also demonstrate the use of 'non-strict' Rao-Blackwellisation. We show that the unscented Kalman filter (UKF) and UKF in a particle filtering framework outperform the generic particle filter, the extended Kalman filter (EKF) and EKF in a particle filtering framework with respect to accuracy in terms of estimation RMSE and sensitivity with respect to choice of network structure. Especially we demonstrate the superiority of UKF in a PF framework when our beliefs of how data was generated are wrong. Furthermore, we investigate the influence of data noise in the watertank simulation using UKF and PFUKD and show that the algorithms are more sensitive to changes in the measurement noise level that the process noise level. Theory and implementation is based on (v.d. Merwe et al., 2000).

Andersen, Morten Nonboe↗

DOE OSTI2025

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Simulation Center for Runaway Electron Avoidance and Mitigation (SCREAM SciDAC) (Technical Final Report)

Runaway electrons can severely damage the plasma facing components on ITER during a major disruption and pose a major risk for tokamak fusion. It has been recognized that an adequate disruption mitigation system (DMS) is essential for the safe operation of ITER. The United States is responsible for the design and implementation of the disruption mitigation system on ITER, and in July 2016 the Simulation Center for Runaway Electron Avoidance and Mitigation (SCREAM) was launched by DOE, in a joint Fusion Energy Sciences (FES) and Advanced Scientific Computing Research (ASCR) collaboration. SCREAM was a comprehensive theory and simulation SciDAC center that provided physics guidance in the avoidance and mitigation of runaway electrons, and in tandem with domestic and international experiments, helped establish the qualitative and quantitative bases for safe operational scenarios and viable mitigation techniques. The SCREAM center assembled a national team of experts in runaway electron physics, tokamak disruptions, magnetohydrodynamic (MHD) simulation, and advanced algorithms and computing. The team combined advanced simulation and analysis capability facilitated by direct participation of ASCR SciDAC institutes with theoretical models and code development by FES scientists to focus on the runaway risk for ITER and tokamaks in general. The research scope was focussed on integrated simulations of kinetic runaway electrons, including MHD and fluid models of impurity transport, within a research plan guided by theory. The specific research tasks were (1) establish the fundamental physics of runaway generation, saturation, and dynamical evolution in a tokamak; (2) examine the critical path toward runaway avoidance; and (3) investigate the viability and effectiveness of the leading candidate schemes for runaway mitigation. In all three areas, members of the team carried out scoping studies that established the readiness for rapid and critical advances, especially in the deployment and further development of large-to extreme-scale simulation tools. Our multi-pronged computational approach included (1) relativistic Fokker-Planck solvers with discretization in phase space, (2) self-consistent particle-in-cell techniques, (3) particle-based Monte-Carlo, and (4) MHD-particle hybrid simulations. Cross-check between these different methods provided an additional means for verification and further bolstered the fidelity of our physics prediction. Validation against experimental results brings confidence to the predictive capability for ITER and frequently leads to new ideas for understanding and mitigating the thermal quench driven runaway electron phenomenon.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories

Here, the accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH 3 ) molecule and the nucleophilic substitution (S N 2) reaction F – + CH 3 F → FCH 3 + F – . We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Iyer, Gopal R.↗